Handbook of Conformal Mapping with Computer-Aided Visualization: 1st Edition (Hardback) book cover

Handbook of Conformal Mapping with Computer-Aided Visualization

1st Edition

By Valentin I. Ivanov, Michael K. Trubetskov

CRC Press

368 pages

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Hardback: 9780849389368
pub: 1994-12-16
$300.00
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Description

This book is a guide on conformal mappings, their applications in physics and technology, and their computer-aided visualization. Conformal mapping (CM) is a classical part of complex analysis having numerous applications to mathematical physics. This modern handbook on CM includes recent results such as the classification of all triangles and quadrangles that can be mapped by elementary functions, mappings realized by elliptic integrals and Jacobian elliptic functions, and mappings of doubly connected domains. This handbook considers a wide array of applications, among which are the construction of a Green function for various boundary-value problems, streaming around airfoils, the impact of a cylinder on the surface of a liquid, and filtration under a dam.

With more than 160 domains included in the catalog of mapping, Handbook of Conformal Mapping with Computer-Aided Visualization is more complete and useful than any previous volume covering this important topic. The authors have developed an interactive ready-to-use software program for constructing conformal mappings and visualizing plane harmonic vector fields. The book includes a floppy disk for IBM-compatible computers that contains the CONFORM program.

Table of Contents

Mathematics: The Theory of Conformal Mappings

Complex Plane, Domains and Curves on It

The Analytic Functions of a Complex Variable

Conjugate Harmonic Functions

The Geometric Meaning of the Derivative; Isogonal and Local Conformal Mappings

Univalent Analytic Functions. Conformal Mappings of Domains

General Principles of the Theory of Conformal Mappings

Conformal Mappings Realized by the Basic Elementary Functions

Isothermic Coordinates. Differential Operators in the Isothermic Coordinates

Mappings of Lunes

The Construction of Conformal Mappings with the Help of the Boundary Correspondence Principle

The Construction of Conformal Mappings of Curvilinear Strips with the Help of an Analytic Continuation of a Function from the Real Axis

The Mapping of Polygonal Domains. Schwarz-Christoffel Integral

Mappings of Rectangular Domains. Elliptic Integrals and Elliptic Functions

Conformal Mapping of Doubly Connected Domains

Physics: Applications of Conformal Mappings

Insight into Plane Harmonic Vector Field

Plane Harmonic Vector Fields in Physics

Complex Potential

Boundary-Value Problems for Harmonic Functions

The Construction of a Green Function of the Dirichlet Problem

The Green Function of the Neumann Problem

The Green Function of a Mixed Boundary-Value Problem

Point Source and Sink in the Dirichlet Problem

Point Source and Sink in the Neumann Problem

Plane Robin Problem

The Flow in a Curvilinear Angular Domain. Streaming Around an Infinite Curve

The Flow in a Curvilinear Strip

The Flow in a Curvilinear Strip with N Branches

The Flow Running onto an Infinite Curve and Branching on It

Irrotational Streaming Around a Finite Contour

Mixed Boundary-Value Problem in a Curvilinear Angular Domain. The Simplest Problem of the Filtration Theory

Distribution of the Electric Current in a Plate in the Presence of Two Non-Point Electrodes at Its Boundary

The General Problem on the Streaming Around a Finite Contour

The Problem on the Impact of a Solid Cylinder upon the Surface of a Non-Compressible Liquid

The Flow with Branching in a Curvilinear Strip with N Branches

Practice: Catalog of Conformal Mappings

Finite Domains

Exteriors of Finite Contours

Curvilinear Angular Domains

Curvilinear Strips

Curvilinear Strips with N Branches

Appendix: Program CONFORM

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT037000
MATHEMATICS / Functional Analysis